Reporting "unprecedented levels" of interest in its ships, the company said Monday it booked more than 565,000 passengers for upcoming voyages, a 17 percent boost compared to the same period last year.

Carnival also said traffic to its website reached an all-time high, with 13 million visits during the one-month period.

"We are seeing heavy sales growth in all channels," Carnival President and CEO Gerry Cahill said in a statement, crediting ship upgrades, "very attractive promotions" and a new advertising campaign as some of the factors that led to the record January.

Carolyn Spencer Brown, editor-in-chief of CruiseCritic.com, said Carnival's new concert series, Caribbean- and American-inspired dining menus, and the "Seuss at Sea" programs for kids are persuading new customers to give cruising a try.

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Stewart Chiron, CEO of Cruiseguy.com, also said he was not surprised by Carnival's good fortunes.

"There are terrific cruise deals out there, but nothing really out of the ordinary," Chiron said.

"Cold weather is always a plus, and people enjoy top value for their hard-earned vacation dollars. Carnival's safety upgrades … and overall consumer confidence certainly make an impact. Bottom line, consumers have spoken by their bookings and they're confident in the Carnival brand."

Carnival's news also comes just days after a norovirus outbreak—which the Centers for Disease Control and Prevention called one of the biggest in 20 years—struck the Royal Caribbean ship Explorer of the Seas. Almost 700 people were sickened, forcing the voyage to end early. A norovirus bug also infected a Princess Cruises ship last week, sickening at least 176 people on board.

But such incidents don't seem to be putting travelers off vacations as sea. Some 21.7 million passengers are expected to take a cruise this year, up from 21.3 million who cruised in 2013, according to the Cruise Lines International Association.